instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Which is the fifth biggest value? (a) -58 (b) 4 (c) 15 (d) -0.4 (e) -1/407\n | a\n | ibivibiv/math_instruct | |
Suppose 12 = 5*i - 4*i. Suppose 0 = -4*g + 8*g - i. Find the second derivative of b + 2*b**5 - b**5 - g*b**5 wrt b.\n | -40*b**3\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) 39 (b) 4 (c) 3\n | a\n | ibivibiv/math_instruct | |
What is the result of the following expression?
5.3 - 8.54 | -3.24 | ibivibiv/math_instruct | |
In base 9, what is -257 + -3474540?\n | -3474807\n | ibivibiv/math_instruct | |
What is the tens digit of 5827977?\n | 7\n | ibivibiv/math_instruct | |
Let u = 1272 - 1119. What is the smallest common multiple of 18 and u?\n | 306\n | ibivibiv/math_instruct | |
Is 17 a factor of 1446003?\n | True\n | ibivibiv/math_instruct | |
Two letters picked without replacement from kxxxxxxkkxkkxxkxxxx. What is prob of sequence kx?\n | 13/57\n | ibivibiv/math_instruct | |
What is 1130230233 (base 4) in base 12?\n | 163893\n | ibivibiv/math_instruct | |
Let n be (98/90 + -1)*-5. Let m = 310 + -314. Put 5, m, 7, n in decreasing order.\n | 7, 5, n, m\n | ibivibiv/math_instruct | |
Let w(j) = -j**3 + 6*j**2 + 2*j + 24. Let v be w(5). What is the highest common factor of v and 767?\n | 59\n | ibivibiv/math_instruct | |
What is f in -5*f**3 - 4730*f**2 + 62405*f + 67130 = 0?\n | -959, -1, 14\n | ibivibiv/math_instruct | |
Let v = -43.9166 + 0.0166. Let p = v - -43.7. Which is the closest to 0? (a) p (b) 2 (c) -2/7 (d) -0.02\n | d\n | ibivibiv/math_instruct | |
Let h = 848.91475 - 983.918. Let o = 135 + h. Round o to three decimal places.\n | -0.003\n | ibivibiv/math_instruct | |
Suppose -21*g + 8*g = -1833. Let w = -79 - -82. Suppose 5*u + 74 = j, -4 - 298 = -w*j - 5*u. What is the highest common divisor of g and j?\n | 47\n | ibivibiv/math_instruct | |
What is the nearest to -1 in -2/11, -4, -1/13, -0.08?\n | -2/11\n | ibivibiv/math_instruct | |
Calculate 4*(-8)/(-96)*4/2.\n | 2/3\n | ibivibiv/math_instruct | |
Let k(y) be the second derivative of -3*y**5/160 + 5*y**4/32 - y**3/2 + 3*y**2/4 - 9*y - 4. Let k(r) = 0. Calculate r.\n | 1, 2\n | ibivibiv/math_instruct | |
Let z = 0.34456 + -0.34456. Which is the second biggest value? (a) z (b) 0.5 (c) -9 (d) -4/7\n | a\n | ibivibiv/math_instruct | |
Calculate 761955395*-0.4.\n | -304782158\n | ibivibiv/math_instruct | |
Suppose -7*n + n = -66. Calculate the highest common divisor of n and 88.\n | 11\n | ibivibiv/math_instruct | |
Solve 0 = -6*m + 1988 - 1964 for m.\n | 4\n | ibivibiv/math_instruct | |
b"What is the cth term of -7139, -14612, -22087, -29564, -37043?\n" | -c**2 - 7470*c + 332\n | ibivibiv/math_instruct | |
6413356.641 - -11.565\n | 6413368.206\n | ibivibiv/math_instruct | |
Let o(q) = 2*q**2. Let s(u) = 3722*u. Calculate s(o(f)).\n | 7444*f**2\n | ibivibiv/math_instruct | |
Solve 109*b - 110*b = 5 for b.\n | -5\n | ibivibiv/math_instruct | |
What is 22.6556112 rounded to three decimal places?\n | 22.656\n | ibivibiv/math_instruct | |
Let a = 142 - 140. Solve 5*p + 5 = -20, -a*p = 2*t + 4 for t.\n | 3\n | ibivibiv/math_instruct | |
What is ((-374)/(-24))/17*(-1)/((-1)/(-2))?\n | -11/6\n | ibivibiv/math_instruct | |
Let o(k) = -115*k**3 + 3*k**2 - 2*k - 5. Let b(u) = 115*u**3 - 4*u**2 + 2*u + 6. Let s(l) = 4*b(l) + 5*o(l). Let j be (-7)/5 - (-4)/10. Is s(j) prime?\n | False\n | ibivibiv/math_instruct | |
What is the value of -1 + 1*-1 + 92 + -87?\n | 3\n | ibivibiv/math_instruct | |
Solve -w + 90*b = 4*w - 695, 3*w + 4*b = 73 - 120 for w.\n | -5\n | ibivibiv/math_instruct | |
Find the third derivative of 3*c**3*g**3 - 14*c**3*g**2*p + 4*c**3*g*p - c**2*g**3 + 5*c**2 - 19*c*g**3*p wrt c.\n | 18*g**3 - 84*g**2*p + 24*g*p\n | ibivibiv/math_instruct | |
Four letters picked without replacement from sspmlbsplssplpsppl. What is prob of sequence lmlb?\n | 1/6120\n | ibivibiv/math_instruct | |
Let f(w) = -3*w - 3. Let s be f(-2). Suppose -s*c + c = 0. Suppose -4*i + 6 + 26 = c. Calculate the highest common divisor of 24 and i.\n | 8\n | ibivibiv/math_instruct | |
8*(-4)/16*2/(-2*8)\n | 1/4\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 678 and 18.\n | 6\n | ibivibiv/math_instruct | |
Let t = -2/649 + -643/1947. What is the second smallest value in t, 2, 0.9?\n | 0.9\n | ibivibiv/math_instruct | |
Solve -12 = -2342*d + 2339*d, 5*x = -3*d + 17 for x.\n | 1\n | ibivibiv/math_instruct | |
Simplify (-1*(sqrt(1300) + -6*sqrt(1300)*1))/((sqrt(32)/sqrt(4)*2)/(sqrt(72) - (sqrt(72) + -1*sqrt(72)))).\n | 75*sqrt(13)\n | ibivibiv/math_instruct | |
Solve 869 = -78*h - 143 + 76 for h.\n | -12\n | ibivibiv/math_instruct | |
Which is smaller: -190256 or -190254?\n | -190256\n | ibivibiv/math_instruct | |
Suppose 7*n - 2*n + 4693 = 24*n. Suppose -3*h - 20 + 3 = -2*l, -3*l + h + 36 = 0. Calculate the greatest common factor of n and l.\n | 13\n | ibivibiv/math_instruct | |
Which is the closest to -11? (a) 15 (b) 1/8 (c) 14/197\n | c\n | ibivibiv/math_instruct | |
What is 401 minutes after 4:01 PM?\n | 10:42 PM\n | ibivibiv/math_instruct | |
Let n be (-3 - (3 - 2)) + 13 + -7. Suppose -k = -4*u + 225, -3*u = 2*u - n*k - 282. Let g(j) = -88*j + 56. Let w(b) = 8*b - 5. Determine u*w(o) + 5*g(o).\n | 8*o\n | ibivibiv/math_instruct | |
Solve -2*z + 4 = 5*l, 2*z - 32*l + 31*l - 4 = 0 for z.\n | 2\n | ibivibiv/math_instruct | |
What is 0.0000882990507 rounded to 5 dps?\n | 0.00009\n | ibivibiv/math_instruct | |
What is next in -20, -22, -24, -26?\n | -28\n | ibivibiv/math_instruct | |
Let q(w) = 26*w + 19. Let y be q(-1). Let m be (-2 - -6) + 65240028/y. Round m to the nearest 1000000.\n | -9000000\n | ibivibiv/math_instruct | |
Which is the closest to 8/3? (a) 0.4 (b) 1 (c) 1/3\n | b\n | ibivibiv/math_instruct | |
b"What is the th term of -228, -456, -684, -912?\n" | -228*b\n | ibivibiv/math_instruct | |
Expand (2*d - 2*d - d**4)*(10 + 0*d + 2*d - 4*d).\n | 2*d**5 - 10*d**4\n | ibivibiv/math_instruct | |
Find the common denominator of -1/426865 and -36/305317.\n | 90068515\n | ibivibiv/math_instruct | |
Let t(d) = 2*d**3 - 2*d**2 - 25*d + 168. Calculate the least common multiple of 92 and t(4).\n | 3772\n | ibivibiv/math_instruct | |
Let g(c) = -2*c - 7. Let k be g(-5). Let m(u) = 5*u. Let x be m(k). Suppose 72 = 4*q - 408. What is the highest common divisor of x and q?\n | 15\n | ibivibiv/math_instruct | |
Let h = -3631 + 13811. Suppose -5*p + 1905 = 5*b - h, 2*b = 5*p + 4806. Is b a composite number?\n | True\n | ibivibiv/math_instruct | |
Let t(i) be the second derivative of -5*i**4/12 - 2*i**3/3 + 9*i**2/2 + 53*i. Let d be t(-3). Is -145/6 less than d?\n | True\n | ibivibiv/math_instruct | |
Which is greater: 24593/97 or 255?\n | 255\n | ibivibiv/math_instruct | |
Two letters picked without replacement from pppmmmpppmpmmmppmmpm. Give prob of sequence mm.\n | 9/38\n | ibivibiv/math_instruct | |
Simplify (2 + -4 + sqrt(176)*-1 + (sqrt(176)*2*6 - sqrt(176)) + sqrt(176) + (sqrt(176) - (-1*sqrt(176) + 1)))**2*-4.\n | -119012 + 1248*sqrt(11)\n | ibivibiv/math_instruct | |
Let w be (4/(-9))/(68/(-306)). Suppose t - 3 = -0*t. Let o = 2 + t. Solve o*i - 2*c + 32 = w*c, -5*c = -5*i - 35 for i.\n | -4\n | ibivibiv/math_instruct | |
A math student needs to solve the differential equation y'' - 4y = 0, given that y(0) = 2 and y(0) = -1. | To solve the given differential equation y'' - 4y = 0, we first find the characteristic equation, which is:
r^2 - 4 = 0
This is a quadratic equation, and we can solve for r:
(r - 2)(r + 2) = 0
So, the roots are r1 = 2 and r2 = -2.
Now, we can write the general solution of the given differential equation as:
y(x) ... | ibivibiv/math_instruct | |
What is the billions digit of 1956182521?\n | 1\n | ibivibiv/math_instruct | |
What is -0.000032727 rounded to six dps?\n | -0.000033\n | ibivibiv/math_instruct | |
What is the result of the following expression?
59.6138 % 13.2703 | 6.5326 | ibivibiv/math_instruct | |
Let b = 28.5 + -28. Let j be 10/24 - 2/8. What is the second biggest value in 6, j, -1, b?\n | b\n | ibivibiv/math_instruct | |
Let g be 1 + -3*(0 + 1). Let l be (0 - 0)*(g - -1). Find the second derivative of l*w + 3*w**4 + w - 5*w**4 wrt w.\n | -24*w**2\n | ibivibiv/math_instruct | |
What is the nearest to 0.5 in -0.7, 8, -0.5, 1?\n | 1\n | ibivibiv/math_instruct | |
Let t be (-16 + 21)*(-11)/(-5). Let k(c) = 2 - 2*c**3 + 12 + 12*c**2 - 12*c + c**3. Let g be k(t). Solve 0 = -g*l - 2*l + 10 for l.\n | 2\n | ibivibiv/math_instruct | |
Let y(i) = -26*i + 85. Let r be y(9). Put -4/5, -2, r in ascending order.\n | r, -2, -4/5\n | ibivibiv/math_instruct | |
Suppose 39*u**3/5 - 16698*u**2/5 - 8275884*u/5 + 1273608/5 = 0. Calculate u.\n | -294, 2/13, 722\n | ibivibiv/math_instruct | |
Let t(i) = -i + 85. Let f(p) = 4*p - 306. Let v(s) = -5*f(s) - 18*t(s). Let w(r) = -25*r**2 - 13. What is w(v(j))?\n | -100*j**2 - 13\n | ibivibiv/math_instruct | |
-8 (base 16) to base 6\n | -12\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-88.666 / -28.856 | 3.0727 | ibivibiv/math_instruct | |
Suppose -4/3*m**2 - 32/3 - 8*m = 0. What is m?\n | -4, -2\n | ibivibiv/math_instruct | |
Let x(j) = 4*j**2 - 3*j - 1. Let t(g) = -13*g - 9*g + 23*g - g**2 + 0*g**2. Let f be (0 - 1)/(2/6). Calculate f*t(z) - x(z).\n | -z**2 + 1\n | ibivibiv/math_instruct | |
Suppose 0 = -u + 3*x + 106912, u - 105356 - 1550 = x. Is u composite?\n | False\n | ibivibiv/math_instruct | |
Which is the fifth biggest value? (a) 0.2 (b) -0.3 (c) 6 (d) 26275.2 (e) 5\n | b\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 63 and 340/6 + 4/(-6).\n | 504\n | ibivibiv/math_instruct | |
Sum 172021 and -0.18.\n | 172020.82\n | ibivibiv/math_instruct | |
Rearrange -5*s**3 + s**2 + 5*s**3 + 53 - s**4 - 52 - 12*s**3 + s**2 to the form f*s**2 + d + l*s**3 + m*s + o*s**4 and give l.\n | -12\n | ibivibiv/math_instruct | |
List the prime factors of 501.\n | 3, 167\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 360 and 180.\n | 360\n | ibivibiv/math_instruct | |
How many months are there in 61756.61 decades?\n | 7410793.2\n | ibivibiv/math_instruct | |
Let f = -2 + 7. Suppose -g + 3*v + 91 = 0, g = 2*g - f*v - 85. Suppose 5*r + 3*t = t + 125, g = 4*r - t. Is r a prime number?\n | False\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Point such that sum of squares of distance to other points are minimized
I need to find $P(x,y)$ such that sum of squares of distance to points $A(3,4), B(20,8), C(4,24)$ is minimized. So I had a general expression of dist... | The problem at hand involves finding the point P(x,y) that minimizes the sum of the squares of its distances to three given points A(3,4), B(20,8), and C(4,24). This can be approached as a multivariable calculus optimization problem, where we aim to minimize the function S representing the sum of the squared distances... | ibivibiv/math_instruct | |
Solve -2*l + 3 = -328*s + 327*s, -5*s - 3*l = 2 for s.\n | -1\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {x: 1, u: 2, f: 1, w: 5}. Give prob of picking 1 f and 2 w.\n | 5/42\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"## How to find diameter from volume x length
Geometric formulae, word problems, theorems and proofs, etc.
### How to find diameter from volume x length
The following question is in a chemistry textbook I have been using as... | To solve the problem provided, let's break it down step by step while ensuring rigorous understanding and engagement through detailed explanations. We will begin by finding the cross-sectional area of the cylindrical tube using its volume and length, then proceed to calculate the radius, and finally determine the diam... | ibivibiv/math_instruct | |
Let n = 0.11 + -4.11. Let g = -4.0009 - n. Round g to 4 dps.\n | -0.0009\n | ibivibiv/math_instruct | |
Is 49 a factor of 1617?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = -2*f + 13 + 65. Let k(x) = -x**2 + 8*x - 3. Let p be k(4). What is the greatest common factor of f and p?\n | 13\n | ibivibiv/math_instruct | |
What comes next: 5799, 11644, 17539, 23478, 29455, 35464, 41499, 47554?\n | 53623\n | ibivibiv/math_instruct | |
What is prob of picking 3 d and 1 w when four letters picked without replacement from {h: 4, d: 3, f: 2, w: 2}?\n | 1/165\n | ibivibiv/math_instruct | |
Let z(k) = -3247*k**2 - 4258*k. Let c(s) = -9741*s**2 - 12758*s. Let m(n) = -4*c(n) + 11*z(n). Find the second derivative of m(w) wrt w.\n | 6494\n | ibivibiv/math_instruct | |
Let u(o) = 805*o - 107800. Give u(134).\n | 70\n | ibivibiv/math_instruct | |
What is 31/2 of a meter in millimeters?\n | 15500\n | ibivibiv/math_instruct | |
What is the third smallest value in -0.08, 4, 0.1, -2/11, 13, -10?\n | -0.08\n | ibivibiv/math_instruct |
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